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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "\n",
    "import scipy.linalg as la\n",
    "import scipy\n",
    "from scipy.linalg import expm #, sinm, cosm\n",
    "\n",
    "import sympy\n",
    "from sympy import Matrix\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "source": [
    "# the initial value problem\n",
    "## $ \\frac{dU}{dt} = AU(t) , t\\subset[T_{start},T_{max}] , U(0)=U_0 $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([ [1,2],[-2,2] ])\n",
    "A1 = np.array([ [0.5,0],[-2,1] ])\n",
    "A2 = np.array( [ [0.2,2],[0,1] ])\n",
    "U0 = np.array([[1],[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "40"
      ]
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "DeltaT = 0.0126\n",
    "T_start = 1.0\n",
    "T_max = 1.5\n",
    "t = np.arange(T_start,T_max,DeltaT)\n",
    "int(t.shape[0])"
   ]
  },
  {
   "source": [
    "# Calculate the exact solution\n",
    "## $ U(t)=e^{-At} U_0 $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[-2.41198230e-01 -2.40120911e-01 -2.38859112e-01 -2.37420855e-01\n  -2.35814031e-01 -2.34046394e-01 -2.32125562e-01 -2.30059013e-01\n  -2.27854083e-01 -2.25517968e-01 -2.23057716e-01 -2.20480233e-01\n  -2.17792275e-01 -2.15000454e-01 -2.12111232e-01 -2.09130922e-01\n  -2.06065689e-01 -2.02921548e-01 -1.99704365e-01 -1.96419857e-01\n  -1.93073591e-01 -1.89670986e-01 -1.86217312e-01 -1.82717692e-01\n  -1.79177100e-01 -1.75600367e-01 -1.71992177e-01 -1.68357068e-01\n  -1.64699437e-01 -1.61023538e-01 -1.57333485e-01 -1.53633252e-01\n  -1.49926675e-01 -1.46217454e-01 -1.42509154e-01 -1.38805208e-01\n  -1.35108915e-01 -1.31423448e-01 -1.27751848e-01 -1.24097034e-01]\n [ 8.16160979e-02  7.35958912e-02  6.58043994e-02  5.82404213e-02\n   5.09025874e-02  4.37893677e-02  3.68990791e-02  3.02298925e-02\n   2.37798399e-02  1.75468216e-02  1.15286128e-02  5.72287055e-03\n   1.27140194e-04 -5.26113819e-03 -1.04446235e-02 -1.54260673e-02\n  -2.02083082e-02 -2.47942653e-02 -2.91869333e-02 -3.33893763e-02\n  -3.74047225e-02 -4.12361589e-02 -4.48869264e-02 -4.83603144e-02\n  -5.16596561e-02 -5.47883237e-02 -5.77497240e-02 -6.05472935e-02\n  -6.31844946e-02 -6.56648110e-02 -6.79917440e-02 -7.01688082e-02\n  -7.21995280e-02 -7.40874338e-02 -7.58360587e-02 -7.74489347e-02\n  -7.89295899e-02 -8.02815448e-02 -8.15083099e-02 -8.26133824e-02]]\n"
     ]
    }
   ],
   "source": [
    "Ut = np.zeros((2,int(t.shape[0])))\n",
    "i = 0\n",
    "for dti in t :\n",
    "    exact_solution = expm(A*-dti) @ U0\n",
    "    # print(exact_solution.shape) # (2, 1)\n",
    "    Ut[0,i] = exact_solution[0,0]\n",
    "    Ut[1,i] = exact_solution[1,0]\n",
    "    i+=1\n",
    "print(Ut)"
   ]
  },
  {
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   "execution_count": 5,
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot( t, Ut[0,:],'r--',           label='exact solution')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure()\n",
    "plt.plot( t, Ut[1,:],'r--',           label='exact solution' )\n",
    "plt.legend()"
   ]
  },
  {
   "source": [
    "# Calculate the first order accuracy solution\n",
    "## $ U(t)=e^{-A_1t} e^{-A_2t} U_0 $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2086225c820>"
      ]
     },
     "metadata": {},
     "execution_count": 6
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "Ut_FirstOrder = np.zeros((2,int(t.shape[0])))\n",
    "i = 0\n",
    "for dti in t :\n",
    "    FirstOrder_solution = expm(A1*-dti) @ expm(A2*-dti) @ U0\n",
    "\n",
    "    Ut_FirstOrder [0,i] = FirstOrder_solution[0,0]\n",
    "    Ut_FirstOrder [1,i] = FirstOrder_solution[1,0]\n",
    "    i+=1\n",
    "\n",
    "plt.plot( t, Ut_FirstOrder[0,:],'k',  label='First Order accuracy')\n",
    "plt.plot( t, Ut[0,:],'r--',           label='exact solution')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure()\n",
    "plt.plot( t, Ut_FirstOrder[1,:],'k',  label='First Order accuracy')\n",
    "plt.plot( t, Ut[1,:],'r--',           label='exact solution' )\n",
    "plt.legend()"
   ]
  },
  {
   "source": [
    "# Calculate the second order accuracy solution\n",
    "## $ U(t)=e^{-\\frac{1}{2}*A_1t} e^{-A_2t} e^{-\\frac{1}{2}*A_1t} U_0 $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x20862313ca0>"
      ]
     },
     "metadata": {},
     "execution_count": 7
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "Ut_SecondOrder = np.zeros((2,int(t.shape[0])))\n",
    "i = 0\n",
    "for dti in t :\n",
    "    SecondOrder_solution = expm(A1*-dti*0.5) @ expm(A2*-dti) @ expm(A1*-dti*0.5) @ U0\n",
    "\n",
    "    Ut_SecondOrder [0,i] = SecondOrder_solution[0,0]\n",
    "    Ut_SecondOrder [1,i] = SecondOrder_solution[1,0]\n",
    "    i+=1\n",
    "\n",
    "\n",
    "plt.plot( t, Ut_SecondOrder[0,:],'b', label='Second Order accuracy')\n",
    "plt.plot( t, Ut_FirstOrder[0,:],'k',  label='First Order accuracy')\n",
    "plt.plot( t, Ut[0,:],'r--',           label='exact solution')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure()\n",
    "plt.plot( t, Ut_SecondOrder[1,:],'b', label='Second Order accuracy')\n",
    "plt.plot( t, Ut_FirstOrder[1,:],'k',  label='First Order accuracy')\n",
    "plt.plot( t, Ut[1,:],'r--',           label='exact solution' )\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "source": [
    "# Calculate the G·Strang's second order accuracy solution\n",
    "# $ U(n\\Delta t)  \\approx  [ e^{-\\frac{\\Delta t}{2}*A_2} e^{-A_1 \\Delta t} e^{-\\frac{\\Delta t}{2}*A_2} ]^n U_0 $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def loop(n):\n",
    "    const = expm(-0.5*DeltaT*A2) @ expm(-DeltaT*A1) @ expm(-0.5*DeltaT*A2)\n",
    "    resul = 1\n",
    "    for i in range(1,n+1):\n",
    "        resul*=const\n",
    "\n",
    "    return resul\n",
    "def StrangOplitting(n):\n",
    "    Ut_Strang = loop(n) @ U0\n",
    "    return Ut_Strang\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
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     },
     "metadata": {},
     "execution_count": 9
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "Ut_Strang = np.zeros((2,int(t.shape[0]) ))\n",
    "i = 0\n",
    "for delta_t in t :\n",
    "    i+=1\n",
    "    solution = StrangOplitting(i)\n",
    "\n",
    "    Ut_Strang[0,i-1] = solution[0,0]\n",
    "    Ut_Strang[1,i-1] = solution[1,0]\n",
    "    \n",
    "\n",
    "plt.plot( t, Ut_Strang[0,:] ,'g',     label='Strang Second Order accuracy')\n",
    "plt.plot( t, Ut_SecondOrder[0,:],'b', label='Second Order accuracy')\n",
    "plt.plot( t, Ut_FirstOrder[0,:],'k',  label='First Order accuracy')\n",
    "plt.plot( t, Ut[0,:],'r--',           label='exact solution')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure()\n",
    "plt.plot( t, Ut_Strang[1,:],'g',      label='Strang Second Order accuracy')\n",
    "plt.plot( t, Ut_SecondOrder[1,:],'b', label='Second Order accuracy')\n",
    "plt.plot( t, Ut_FirstOrder[1,:],'k',  label='First Order accuracy')\n",
    "plt.plot( t, Ut[1,:],'r--',           label='exact solution' )\n",
    "plt.legend()"
   ]
  },
  {
   "source": [
    "expm(3*np.array([[1,0],[0,5]]))"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": 10,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[2.00855369e+01, 0.00000000e+00],\n",
       "       [0.00000000e+00, 3.26901737e+06]])"
      ]
     },
     "metadata": {},
     "execution_count": 10
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}